What does "catch-up" mean? Will they ever be as powerful as advanced as the hardcore cares are today (2013)? Yes, they will be. Will they catch-up to hardcore games of the future (2023?). No they won't.
But that's irrelevant. What matters more is if they will catch-up to being "good enough", and that is likely to happen.
I personally think WebGL IS good enough to make quality games, I have no issue with it. I just don't think it will catch-on with the gaming public for other reasons. Look at how much resistance there was to Microsoft's 'always-on' feature of Xbox One, to the resistance to DRM that calls home (it is annoying if you're trying to play a game somewhere that you have no connection), and then the requirement that the developer also maintain infrastructure.
The current system, where you create something native using a cross-platform toolkit, then distribute it once, and the user has it forever - this is what gamers are used to, and what they like. And I admit, it's nice being able to play games when I have no internet connection. I don't think this paradigm is necessarily the best one, but it certainly has its merits.
But that's irrelevant. What matters more is if they will catch-up to being "good enough", and that is likely to happen.